论文标题
某些循环图的分级betti数字
Graded Betti numbers of some circulant graphs
论文作者
论文摘要
令$ g $为循环图$ c_n（s）$，带有$ s \ subseteq \ {1，2，\ dots，\ lfloor \ frac {n} {2} {2} \ rfloor \} $ \ dots，x_ {n-1}] $ the field $ \ mathbb {k} $。在本文中，我们计算$ \ mathbb {n} $ - 分级的betti数字数量的三个循环图家族的边缘理想$ c_n（1,2，\ dots，\ wideHat {j} {j} {j}，\ dots，\ dots，\ lfloor \ lfloor \ frac {n} n} {2} {2} {2} {2} {2} {2} \ rfloor） $ c_ {lm}（1,2，\ dots，\ wideHat {2l}，\ dots，\ wideHat {3l}，\ dots，\ lfloor \ lfloor \ frac {lm} {2} {2} \ rfloor）$ $ c_ {lm}（1,2，\ dots，\ wideHat {l}，\ dots，\ wideHat {2l}，\ dots，\ wideHat {3l}，\ dots，\ dots，\ lfloor \ lfloor \ frac {lm} {lm} {2} {2} {2} {2} {2} {2} {2} {2} {lm rfloor rfloor）$。还讨论了其他代数和组合属性，例如规律性，投影维度，匹配数字以及此类图被覆盖良好时，还讨论了Cohen-Macaulay，依次依次的Cohen-Macaulay，Buchsbaum和$ S_2 $。
Let $G$ be the circulant graph $C_n(S)$ with $S \subseteq \{1, 2, \dots, \lfloor \frac{n}{2} \rfloor\}$, and let $I(G)$ denote the edge ideal in the polynomial ring $R=\mathbb{K}[x_0, x_1, \dots, x_{n-1}]$ over a field $\mathbb{K}$. In this paper, we compute the $\mathbb{N}$-graded Betti numbers of the edge ideals of three families of circulant graphs $C_n(1,2,\dots,\widehat{j},\dots,\lfloor \frac{n}{2} \rfloor)$, $C_{lm}(1,2,\dots,\widehat{2l},\dots, \widehat{3l},\dots,\lfloor \frac{lm}{2} \rfloor)$ and $C_{lm}(1,2,\dots,\widehat{l},\dots,\widehat{2l},\dots, \widehat{3l},\dots,\lfloor \frac{lm}{2} \rfloor)$. Other algebraic and combinatorial properties like regularity, projective dimension, induced matching number and when such graphs are well-covered, Cohen-Macaulay, Sequentially Cohen-Macaulay, Buchsbaum and $S_2$ are also discussed.
